Heights of 10 year olds, regardless of gender closely follow a normal distribution with mean 55 inches and a standard deviation of 6 inches. (a) What is the probability that a randomly chosen 10-year-old is shorter than 48 inches? (b) What is the probability that a randomly chosen 10-year-old is between 60 and 65 inches? (c) If the tallest 10% of the class is considered very tall, what is the height cutoff for “very tall”?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Heights of 10 year olds, regardless of gender closely follow a
(a) What is the
(b) What is the probability that a randomly chosen 10-year-old is between 60 and 65 inches?
(c) If the tallest 10% of the class is considered very tall, what is the height cutoff for “very tall”?
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